[script p]31 3 Trigonal
No. 43 [script p]31 Patterson symmetry [script p]-3

symmetry group diagram

Origin on 31

Asymmetric unit 0 ≤ x; 0 ≤ y; 0 ≤ z ≤ 1

Symmetry operations

(1)  1
      (1 | 0, 0, 0)
(2)  3+ (1/3)   0, 0, z
      (3z | 0, 0, 1/3)
(3)  3- (2/3)   0, 0, z
      (3z-1 | 0, 0, 2/3)
 

Generators selected (1); t(0, 0, 1); (2)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

 General:
3 a 1
(1) xyz(2) -yx - yz + 1/3(3) -x + y-xz + 2/3
l: l = 3n

Symmetry of special projections

Along [001]   3

Origin at 0, 0, z
Along [100]   [script p]1
a' = c   
Origin at x, 0, 0
Along [210]   [script p]1
a' = c   
Origin at x1/2x, 0

Maximal non-isotypic non-enantiomorphic subgroups


I[3] [script p]1 (1)1
IIa none
IIbnone

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index


IIc[2] [script p]32 (c' = 2c) (44); [7] [script p]31 (c' = 7c) (43)

Minimal non-isotypic non-enantiomorphic supergroups


I[2] [script p]3112 (47); [2] [script p]61 (54); [2] [script p]64 (57)
II[3] [script p]3 (c' = 1/3c) (42)








































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